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variants of this functions
EllipticTheta






Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[1,z,q] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/09.01.16.0007.01









  


  










Input Form





EllipticTheta[1, Pi (-(1/2) + (-1 + n) z), E^(I Pi \[Tau])]/ EllipticTheta[1, Pi (-(1/2) + z), E^(I Pi \[Tau])] == Product[EllipticTheta[1, Pi (-(1/2) + n z + k \[Tau]), E^(I n Pi \[Tau])]/ EllipticTheta[1, Pi (-(1/2) + k \[Tau]), E^(I n Pi \[Tau])], {k, 1, -1 + n}] Sum[(\[CurlyTheta][k \[Tau], n \[Tau]] E^((n^2 - n - 2 k) I Pi z))/\[CurlyTheta][n z + k \[Tau], n \[Tau]], {k, 1, n - 1}] /; Im[\[Tau]] > 0 && Element[n, Integers] && n >= 1










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18





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